Volume 11, 1999

University of Bialystok

Copyright (c) 1999 Association of Mizar Users

**Christoph Schwarzweller**- University of Tuebingen

- In this article we continue the formalization of concept lattices following [6]. We give necessary and sufficient conditions for a complete lattice to be isomorphic to a given formal context. As a by-product we get that a lattice is complete if and only if it is isomorphic to a concept lattice. In addition we introduce dual formal concepts and dual concept lattices and prove that the dual of a concept lattice over a formal context is isomorphic to the concept lattice over the dual formal context.

- Preliminaries
- The Characterization
- Dual Concept Lattices

- [1]
Grzegorz Bancerek.
Complete lattices.
*Journal of Formalized Mathematics*, 4, 1992. - [2]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Czeslaw Bylinski.
Partial functions.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [6] Bernhard Ganter and Rudolf Wille. \em Formal Concept Analysis. Springer Verlag, Berlin, Heidelberg, New York, 1996. (written in German).
- [7]
Jolanta Kamienska and Jaroslaw Stanislaw Walijewski.
Homomorphisms of lattices, finite join and finite meet.
*Journal of Formalized Mathematics*, 5, 1993. - [8]
Beata Padlewska.
Families of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Christoph Schwarzweller.
Introduction to concept lattices.
*Journal of Formalized Mathematics*, 10, 1998. - [11]
Christoph Schwarzweller.
Noetherian lattices.
*Journal of Formalized Mathematics*, 11, 1999. - [12]
Andrzej Trybulec.
Domains and their Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [14]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [15]
Andrzej Trybulec.
Finite join and finite meet, and dual lattices.
*Journal of Formalized Mathematics*, 2, 1990. - [16]
Wojciech A. Trybulec.
Partially ordered sets.
*Journal of Formalized Mathematics*, 1, 1989. - [17]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [18]
Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989. - [19]
Stanislaw Zukowski.
Introduction to lattice theory.
*Journal of Formalized Mathematics*, 1, 1989.

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